Local product structure for Equilibrium States

1999/11/17 by Renaud Leplaideur · 9 citations
Mathematics · #Mathematical Dynamics and Fractals

paper · pdf · doi:10.1090/s0002-9947-99-02479-4

Abstract

The usual way to study the local structure of Equilibrium State of an Axiom-A diffeomorphism or flow is to use the symbolic dynamic and to push results on the manifold. A new geometrical method is given. It consists in proving that Equilibrium States for Hölder-continuous functions are related to other Equilibrium States of some special sub-systems satisfying a sort of expansiveness. Using different kinds of extensions the local product structure of Gibbs-measure is proven.

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